What is the value of `296xx304`?

Options

A. a)89974
B. b)89874
C. c)79984
D. d)89984

Answer

To find the value of \( 296 \times 304 \), we can use the algebraic identity for the difference of squares. Here’s a step-by-step solution:

### Step 1: Rewrite the numbers
We can express \( 296 \) and \( 304 \) in terms of \( 300 \):
\[ 296 = 300 - 4 \]
\[ 304 = 300 + 4 \]

### Step 2: Apply the difference of squares formula
The expression \( 296 \times 304 \) can be rewritten using the difference of squares formula:
\[ (a - b)(a + b) = a^2 - b^2 \]
Here, let \( a = 300 \) and \( b = 4 \):
\[ 296 \times 304 = (300 - 4)(300 + 4) = 300^2 - 4^2 \]

### Step 3: Calculate \( 300^2 \)
Now, calculate \( 300^2 \):
\[ 300^2 = 90000 \]

### Step 4: Calculate \( 4^2 \)
Next, calculate \( 4^2 \):
\[ 4^2 = 16 \]

### Step 5: Subtract \( 4^2 \) from \( 300^2 \)
Now, substitute these values back into the equation:
\[ 296 \times 304 = 90000 - 16 \]

### Step 6: Perform the subtraction
Finally, perform the subtraction:
\[ 90000 - 16 = 89984 \]

Thus, the value of \( 296 \times 304 \) is \( 89984 \).

### Final Answer
\[ \boxed{89984} \]

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